(x+3)(2x+9)+7(x+3)=

Solution for (x+3)(2x+9)+7(x+3)= equation:

Simplifying
(x + 3)(2x + 9) + 7(x + 3) = 0

Reorder the terms:
(3 + x)(2x + 9) + 7(x + 3) = 0

Reorder the terms:
(3 + x)(9 + 2x) + 7(x + 3) = 0

Multiply (3 + x) * (9 + 2x)
(3(9 + 2x) + x(9 + 2x)) + 7(x + 3) = 0
((9 * 3 + 2x * 3) + x(9 + 2x)) + 7(x + 3) = 0
((27 + 6x) + x(9 + 2x)) + 7(x + 3) = 0
(27 + 6x + (9 * x + 2x * x)) + 7(x + 3) = 0
(27 + 6x + (9x + 2x2)) + 7(x + 3) = 0

Combine like terms: 6x + 9x = 15x
(27 + 15x + 2x2) + 7(x + 3) = 0

Reorder the terms:
27 + 15x + 2x2 + 7(3 + x) = 0
27 + 15x + 2x2 + (3 * 7 + x * 7) = 0
27 + 15x + 2x2 + (21 + 7x) = 0

Reorder the terms:
27 + 21 + 15x + 7x + 2x2 = 0

Combine like terms: 27 + 21 = 48
48 + 15x + 7x + 2x2 = 0

Combine like terms: 15x + 7x = 22x
48 + 22x + 2x2 = 0

Solving
48 + 22x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 11x + x2) = 0

Factor a trinomial.
2((8 + x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-8, -3}